Simple question this week:

Consider a clock with an hour hand and a minute hand. Starting from midnight, how many times do the hands cross each other in 24 hours.

Note, you don't count the starting point of midnight, with the hands overlapping as a crossing, but you do count the last moment, when the two hands overlap at midnight a day later.

Bonus Question:

Normally, clock hands travel clockwise around the clockface. Suppose now that the two hands are travelling in opposite directions. How many times do the hands cross in this case?

## Thursday, 21 March 2019

## Monday, 18 March 2019

### Math at the Movies: x+y

Well, this was a pain in the backside to edit. The film is so tawdry and dull that we kept getting lost on tangents. Fear not though faithful listener, Thomas has edited the two hours of guff down to a single hour of solid... bronze.

If you want to watch x+y, you can follow the link below.

Subscribe via iTunes.

Follow us on twitter @PodcastMathsAt, as well as @ThomasEWoolley and @benmparker.

Today's discussion points include:

From our mouths to your ears, enjoy!- How should you flip a mattress?
- Does the culture you grow up in influence how you learn maths?
- BUMFIT!

If you want to watch x+y, you can follow the link below.

Further reading links:

- As per usual some artistic license was taken with this true story, this website provides the fact behind the fiction;
- Fancy testing yourself with real IMO problems?
- What is the difference between IMO problems and research mathematics?

Subscribe via iTunes.

Follow us on twitter @PodcastMathsAt, as well as @ThomasEWoolley and @benmparker.

## Friday, 15 March 2019

### Answer to Fermat's Room puzzle

A very diffiicult puzzle this week!

Three people guard two doors. You know that:

This is an extension of the famous two person puzzle. Normally, you only have two guards, one tells the truth and one lies. You have to choose and open one of the doors, but you can only ask a single question to one of the guards.

What do you ask so you can pick the door to freedom?

In this case the solution is:

This works by considering the two possible outcomes. Namely:

This puzzle is so famous it's appeared many times in media

The inclusion of the trickster guard, however, changes the puzzle dramatically. Specifically, you questions have to work no matter who is being asked (truth-teller, liar, or trickster). Further, no matter what you ask, you always have to worry about the trickster screwing up your logic.

Thus, one strategy is to identify one person is NOT the trickster. We don't have to identify whether they are truth-teller, or liar.

Call the three gaurds A, B and C. You ask A:

Three people guard two doors. You know that:

- one person always tells the truth;
- one person always lies;
- one person randomly decides whether to tell the truth or lie (assume lies and truth are equally likely);
- the three know amongst themselves who they are.

This is an extension of the famous two person puzzle. Normally, you only have two guards, one tells the truth and one lies. You have to choose and open one of the doors, but you can only ask a single question to one of the guards.

What do you ask so you can pick the door to freedom?

In this case the solution is:

**If I asked what door would lead to freedom, what door would the other guard point to?**This works by considering the two possible outcomes. Namely:

- If you asked the truth-guard, the truth-guard would tell you that the liar-guard would point to the door that leads to death.
- If you asked the liar-guard, the liar-guard would tell you that the truth-guard would point to the door that leads to death.

This puzzle is so famous it's appeared many times in media

The inclusion of the trickster guard, however, changes the puzzle dramatically. Specifically, you questions have to work no matter who is being asked (truth-teller, liar, or trickster). Further, no matter what you ask, you always have to worry about the trickster screwing up your logic.

Thus, one strategy is to identify one person is NOT the trickster. We don't have to identify whether they are truth-teller, or liar.

Call the three gaurds A, B and C. You ask A:

"Is exactly one of these statements true:

If you get back the answer no, then the possibilities are:

Once you have found a person who is not the trickster, just point to a door and ask the person:

"Would your

Thus, reducing the problem to the previous case.

- You are the truth-teller
- B is the trickster

- A is the truth-teller and B is the liar (1. true, 2. false, so one statement true, so answer is yes which truth-teller truthfully gives)
- A is the trickster
- A is the liar and B is the truth-teller (both statements false so answer is no which liar lies about)

If you get back the answer no, then the possibilities are:

- A is the truth-teller and B is the trickster (both statements true, so answer is no which truth-teller truthfully gives)
- A is the trickster
- A is the liar and B is the trickster (1. false, 2. true so one statement true so answer is yes which liar lies about)

Once you have found a person who is not the trickster, just point to a door and ask the person:

"Would your

**exact**opposite say this door leads to freedom?"Thus, reducing the problem to the previous case.

## Tuesday, 5 March 2019

### Maths at the Movies: CUBE

This week is a little different, and I've got to say perhaps one of the most interesting episodes we've ever done!

We are joined by the multi-talented

who uses her research knowledge of evolutionary biology and digital literature to show us how to really write a good movie!

Highlights this week are:

If you're interested in watching CUBE you can follow the Amazon link below.

Further reading links:

Subscribe via iTunes.

Follow us on twitter @PodcastMathsAt, as well as @ThomasEWoolley and @benmparker.

We are joined by the multi-talented

who uses her research knowledge of evolutionary biology and digital literature to show us how to really write a good movie!

Highlights this week are:

- Liz geeking out with Lyle, will they go on holiday together?
- Ben misunderstanding publishing, will he ever get his cheese and wine?
- Thomas reliving his childhood years, when did he stop being so nihilistic

If you're interested in watching CUBE you can follow the Amazon link below.

- Wondering what digital fiction looks like? Well try
*What football will look like in the future*? and prepare to have your horizons expanded. - If you're interested in the future of literature then have a look at Lyle's recent book. It discusses such subjects as: indie publishers, hybrid authors, and fanfiction writers.
- Lyle's also written plenty of digital fiction. Again, this is reading, but not as we know it.
- If you're lazy and got be bothered to read then why not try Lyle's podcast Wonderbox publishing.
- If you've seen CUBE, when not try CUBE ZERO and CUBE 2: Hypercube. They are equally as bonkers!
- The geocities CUBE website that actually investigated the mathematics more than we did!

Subscribe via iTunes.

Follow us on twitter @PodcastMathsAt, as well as @ThomasEWoolley and @benmparker.

## Friday, 1 March 2019

### Puzzle from Fermat's Room

Three people guard two doors. You know that:

Some further rules for the more pedantic:

- one person always tells the truth;
- one person always lies;
- one person randomly decides whether to tell the truth or lie (assume lies and truth are equally likely);
- the three know amongst themselves who they are.

Some further rules for the more pedantic:

- You cannot ask questions like "Will it rain tomorrow?", because neither the truth teller, nor the liar can be sure.
- You cannot ask questions like "What would you answer if I ask you blablabla?", because if you ask the random liar they don't what their next answer will be.
- You cannot ask something like "Will you answer No to this question?", because the truth-teller can't answer this question.
- All decisions must be based on the yes and/or no answers only.
- This puzzle is not about "how to find a way around the rules".

## Thursday, 28 February 2019

### Answer to the Good Will Hunting puzzle

In our Good Will Hunting podcast we asked:

What is the highest number of eggs that you

Turns out this is called the McNuggest number as McNuggets originally came in boxes of this size.

In this case, it turns out that 43 is the largest number you can't make, but how do you prove it?

Well we note that:

44 = 4x6+20

45 = 5x9

46 = 6+2x20

47 = 3x9+20

48 = 8x6

49 = 9+2x20

Since we have 6 consecutive numbers that can all be made from 6, 9 and 20, then every number there after can be made simply by adding an appropriate multiple of 6, e.g. 50 = 44+6, 51 = 45+6, etc.

Simple, no?

What is the highest number of eggs that you

*make, when you have boxes of size 6, 9 and 20?***CAN'T**Turns out this is called the McNuggest number as McNuggets originally came in boxes of this size.

In this case, it turns out that 43 is the largest number you can't make, but how do you prove it?

Well we note that:

44 = 4x6+20

45 = 5x9

46 = 6+2x20

47 = 3x9+20

48 = 8x6

49 = 9+2x20

Since we have 6 consecutive numbers that can all be made from 6, 9 and 20, then every number there after can be made simply by adding an appropriate multiple of 6, e.g. 50 = 44+6, 51 = 45+6, etc.

Simple, no?

## Tuesday, 19 February 2019

### Maths at the Movies: Fermat's Room

Welcome to the strangely erotic episode of Maths at, where we watch the tense, psychological thriller, Fermat's Room (or La HabitaciĆ³n de Fermat, for you Spanish speakers) and we ask the real questions of... WHAT HAPPENED ON THE BOAT?

As per usual, the time line is all wonky. This episode does follow on from A Beautiful Mind, but was recorded a long time after, so although we talk about our lives having changed dramatically, it's only bee two weeks for you and you already know what's happened if you've listened to our Christmas episode. It's so hard living in a linear timeline.

So if you want to know:

If you're interested in watching Fermat's Room and want an easier time than we had in finding it, simply click the Amazon link below.

As per usual, the time line is all wonky. This episode does follow on from A Beautiful Mind, but was recorded a long time after, so although we talk about our lives having changed dramatically, it's only bee two weeks for you and you already know what's happened if you've listened to our Christmas episode. It's so hard living in a linear timeline.

So if you want to know:

- what Liz's ovaries sound like;
- which superpower our hosts would rather have;
- how Ben would overhaul examination procedures,

Further reading links:

- videos of every puzzle from the film;
- a complete writeup of questions and answers from the film
- A duck popcorn maker, should you want such a thing.

Subscribe via iTunes.

Follow us on twitter @PodcastMathsAt, as well as @ThomasEWoolley and @benmparker.

Follow us on twitter @PodcastMathsAt, as well as @ThomasEWoolley and @benmparker.

## Tuesday, 12 February 2019

### Puzzle from Good Will Hunting

Ben's local shop stocks eggs in boxes of capacity 6, 9, or 20 eggs. What is the highest number of eggs that you

For example, you can make 29 with one 9 box and one 20 box, 29=9+20,

you can make 30 with a five 6 boxes, 30=5x6.

but you can't make 31.

For those wanting an extra puzzle, can you

*make?***CAN'T**For example, you can make 29 with one 9 box and one 20 box, 29=9+20,

you can make 30 with a five 6 boxes, 30=5x6.

but you can't make 31.

For those wanting an extra puzzle, can you

*that your answer is correct. Namely, all numbers higher than your chosen integer can be written as a linear combination of 6, 9 or 12.***prove**## Friday, 8 February 2019

### Answer to A Beautiful Mind puzzle

In our podcast episode on A Beautiful Mind
the following question was asked:

Two trains are on the same track. They start 100km apart and head towards each other at a speed of 50km/h.

Whilst these two trains are heading for their collision a fly starts out on the front of one train and zooms directly to the front of the other at a speed of 75km/h (see the animation above). Once the fly reaches the second train it immediately darts back to the front of the first train at the same speed and repeats this back and forth motion until the two trains collide and the fly is squashed on impact.

How far has the fly traveled, before it meets its demise?

One way to approach this problem is through infinite series. Namely, we find how far the fly during the first journey, the second journey, the third journey, etc. and add them all up. Thankfully, there is a fairly nice formula that provides this answer.

However, a much simpler way to calculate the distance is by realising that the changes in direction do not matter. Namely, all we are asking is how far can a fly travel in the hour it takes for the trains to hit each other? Clearly, this is simply 75 km. Sometimes, a moment's thought can save an hour's work!

As mentioned last time, John von Neumann was said to have immediately answered this problem, but when pressed on his solution method he said that he has used the infinite series method. Ah to have the mind of a genius!

This and other aspects of von Neumann's genius are discussed in Raymond Flood's excellent Gresham College talk, below (plus you get a bit of Alan Turing for free, which Thomas is always happy about).

Two trains are on the same track. They start 100km apart and head towards each other at a speed of 50km/h.

Whilst these two trains are heading for their collision a fly starts out on the front of one train and zooms directly to the front of the other at a speed of 75km/h (see the animation above). Once the fly reaches the second train it immediately darts back to the front of the first train at the same speed and repeats this back and forth motion until the two trains collide and the fly is squashed on impact.

How far has the fly traveled, before it meets its demise?

One way to approach this problem is through infinite series. Namely, we find how far the fly during the first journey, the second journey, the third journey, etc. and add them all up. Thankfully, there is a fairly nice formula that provides this answer.

However, a much simpler way to calculate the distance is by realising that the changes in direction do not matter. Namely, all we are asking is how far can a fly travel in the hour it takes for the trains to hit each other? Clearly, this is simply 75 km. Sometimes, a moment's thought can save an hour's work!

As mentioned last time, John von Neumann was said to have immediately answered this problem, but when pressed on his solution method he said that he has used the infinite series method. Ah to have the mind of a genius!

This and other aspects of von Neumann's genius are discussed in Raymond Flood's excellent Gresham College talk, below (plus you get a bit of Alan Turing for free, which Thomas is always happy about).

## Tuesday, 5 February 2019

### Maths at the Movies: Good Will Hunting

Last week we did A Beautiful Mind and now Good Will Hunting. We are really hitting all the well-known maths films at the moment aren't we?

More importantly joining us this week we have the wonderful

This week we touch on such subjects as:

If you're interested in watching Good Will Hunting you can follow the Amazon link below.

Further reading links:

Subscribe via iTunes.

Follow us on twitter @PodcastMathsAt, as well as @ThomasEWoolley and @benmparker.

More importantly joining us this week we have the wonderful

Philanthropist, playboy, billionaire... he is none of this things, but he may have identified the real Will Hunting!

This week we touch on such subjects as:

- Is University a scam?
- Good Will Hunting needs a prequel!
- Will James and Liz ever write a paper about the maths of Dirty Dancing?

If you're interested in watching Good Will Hunting you can follow the Amazon link below.

Further reading links:

- What is the Hadwiger-Nelson problem and who is Aubrey de Grey?
- We also mention the fields of Combinatorics, Graph theory and Fourier theory.

Subscribe via iTunes.

Follow us on twitter @PodcastMathsAt, as well as @ThomasEWoolley and @benmparker.

## Friday, 1 February 2019

### Puzzle from A Beautiful Mind.

A classic puzzle to start our second series. It appears in the background of A Beautiful Mind and it is said that the famous mathematician John von Neumann immediately answered with the correct result. But we'll talk about solutions later!

Two trains are on the same track. They start 100km apart and head towards each other at a speed of 50km/h.

Whilst these two trains are heading for their collision a fly starts out on the front of one train and zooms directly to the front of the other at a speed of 75km/h (see the animation above). Once the fly reaches the second train it immediately darts back to the front of the first train at the same speed and repeats this back and forth motion until the two trains collide and the fly is squashed on impact.

How far has the fly traveled, before it meets its demise?

If you think you have the answer comment below, tweet it to us @PodcastMathsAt, or email us at podcastmaths@gmail.com.

The answer will be posted next week.

Animation illustrating the problem courtesy of MathWorld. |

Two trains are on the same track. They start 100km apart and head towards each other at a speed of 50km/h.

Whilst these two trains are heading for their collision a fly starts out on the front of one train and zooms directly to the front of the other at a speed of 75km/h (see the animation above). Once the fly reaches the second train it immediately darts back to the front of the first train at the same speed and repeats this back and forth motion until the two trains collide and the fly is squashed on impact.

How far has the fly traveled, before it meets its demise?

If you think you have the answer comment below, tweet it to us @PodcastMathsAt, or email us at podcastmaths@gmail.com.

The answer will be posted next week.

## Tuesday, 22 January 2019

### Maths at the Movies: A Beautiful Mind

Ok, so the "Maths at" timeline is a mess.

Sorry about all that. Just pretend that Thomas, Ben and Liz are Time Lords.

Anyway, we had to get there eventually. Probably number one of many science film lists: A Beautiful Mind. The biopic of John Nash, a prodigy behind the field of game theory.

To help us discern our cooperators from our defectors we are joined by the wonderful

If you're interested in watching A Beautiful Mind you can follow the Amazon link below.

Subscribe via iTunes.

Follow us on twitter @PodcastMathsAt, as well as @ThomasEWoolley and @benmparker.

- The Christmas episode was recorded in November.
- The Christmas episode reveals secrets from later on in the series.
- We tried to hide these secrets in the Mean Girls episode, which was recorded around seventh, but released first.
- When we I say that we've had a complaint about Liz's language it from the pi day episode, not the Mean Girls episode.

Sorry about all that. Just pretend that Thomas, Ben and Liz are Time Lords.

Anyway, we had to get there eventually. Probably number one of many science film lists: A Beautiful Mind. The biopic of John Nash, a prodigy behind the field of game theory.

To help us discern our cooperators from our defectors we are joined by the wonderful

So, if you're wondering:

- which queue to join;
- which region in Risk to take;
- or simply how to win at Monpoly,

If you're interested in watching A Beautiful Mind you can follow the Amazon link below.

Further reading links:

Follow us on twitter @PodcastMathsAt, as well as @ThomasEWoolley and @benmparker.

## Tuesday, 8 January 2019

### Maths at the Movies: Mean Girls

Mean girls...

There is no font, size or punctuation mark that does full justice to Thomas' anger.

- Liz tries to convince Thomas that "Do you even go here?" is a funny line;
- Thomas' blood pressure shoots through the roof;
- Ben compares Mean Girls to the New Testament. and Liz compares it to a clockwork orange.

If you're interested in watching Mean Girls then please get help. Go and watch Marvelous Mrs Maisel instead.

However, if you are beyond help that you can follow the Amazon link below.

I mean come on! This meme doesn't even make sense.

Further reading links:

Follow us on twitter @PodcastMathsAt, as well as @ThomasEWoolley and @benmparker.

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